Changes between Version 222 and Version 223 of DatabaseBasedAnalysis/Spectrum

Timestamp:

12/09/19 17:10:21 (5 years ago)

Author:

tbretz

Comment:

--

DatabaseBasedAnalysis/Spectrum

@@ -116 +116 @@
 \[\tau(\delta\theta) = \tau_0\frac{\Delta T(\delta\theta)}{N(\delta\theta)}\]
 
-where \(N(\delta\theta)\) is the number of produced events in the interval \(\delta\theta\) and \(\Delta T(\delta\theta)\) is the total observation time in the same zenith angle interval. \(\tau_0\) is the normalization constant. 
-
-\[\sigma^2(\tau_i) = \left[\frac{d\tau_i}{d\Delta T_i}\sigma(\Delta T_i)\right]^2+\left[\frac{d\tau_i}{dN_i}\sigma(N_i)\right]^2= \tau_i^2\cdot\left[\left(\frac{\sigma(\Delta T_i)}{\Delta T_i}\right)^2+\left(\frac{\sigma(N_i)}{N_i}\right)^2\right]\]
-
-While \(\sigma(\Delta T_i)/\Delta T_i \approx 1\textrm{s}/5\textrm{min}\) is given by the data acquisition and 1s per 5min run, \(\sigma(N_i)/N_i=1/\sqrt{N_i}\) is just the statistical error of the number of events.
+where \(N(\delta\theta)\) is the number of produced events in the interval \(\delta\theta\) and \(\Delta T(\delta\theta)\) is the total observation time in the same zenith angle interval. \(\tau_0\) is the normalization constant. The error on the weight \(\tau=\tau(\delta\theta)\) in each individual \(\theta\)-bin with \(\Delta T=\Delta T(\delta\theta)\) and \(N=N(\delta\theta\)is then
+
+\[\sigma^2(\tau) = \left[\frac{d\tau}{d\Delta T}\sigma(\Delta T)\right]^2+\left[\frac{d\tau}{dN}\sigma(N)\right]^2= \tau^2\cdot\left[\left(\frac{\sigma(\Delta T)}{\Delta T}\right)^2+\left(\frac{\sigma(N)}{N}\right)^2\right]\]
+
+While \(\sigma(\Delta T)/\Delta T \approx 1\textrm{s}/5\textrm{min}\) is given by the data acquisition and 1s per 5min run, \(\sigma(N)/N=1/\sqrt{N}\) is just the statistical error of the number of events.
 
 As the efficiency \(\epsilon(\delta E)\) for an energy interval \(\delta E\) is calculated as